A loading criterion in the elastoplasticity is derived, which is applicable to materials with not only hardening but also softening behavior. Further, the associated flow rule is derived from Ilyushin’s postulate of the non-negative work done during a strain’cycle without the assumption of the existence of a purely elastic domain. These derivations are performed in the framework of the stress space formulation. Besides, irrationalities of the non-associated flow rule incorporating a plastic potential surface different from a yield or a loading surface are described.